# Math Help - this is the applied maximum and minimum problems

1. ## this is the applied maximum and minimum problems

a close rectangular container with a square base is to have a volume of 2250 in^3. teh material for the top and bottom of the container will cost $2 per in^2, and the material for the sides will cost$3 per in^2. Find the dimension of the container of least cost.

2. Originally Posted by redcherry
a close rectangular container with a square base is to have a volume of 2250 in^3. teh material for the top and bottom of the container will cost $2 per in^2, and the material for the sides will cost$3 per in^2. Find the dimension of the container of least cost.
let x = side length of the square base

h = height of the container

$x^2h = 2250$

$C = (2)(2x^2) + (3)(4xh)$

get the cost function in terms of a single variable, take the derivative, and minimize the cost.